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Trigonometrical Equations
easy
જો $\cos \theta = - \frac{1}{{\sqrt 2 }}$અને $\tan \theta = 1$, તો $\theta $ નો વ્યાપક ઉકેલ મેળવો.
A
$2n\pi + \frac{\pi }{4}$
B
$(2n + 1)\,\pi + \frac{\pi }{4}$
C
$n\pi + \frac{\pi }{4}$
D
$n\pi \pm \frac{\pi }{4}$
Solution
(b) $\cos \theta = – \frac{1}{{\sqrt 2 }} \Rightarrow \theta = \frac{{3\pi }}{4},\,\frac{{5\pi }}{4}$;
$\tan \theta = 1 \Rightarrow \theta = \frac{\pi }{4},\,\frac{{5\pi }}{4}$
$\therefore $ The general value is $2n\pi + \frac{{5\pi }}{4}$ or $(2n + 1)\pi + \frac{\pi }{4}$.
Standard 11
Mathematics
